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Explore the intricate connections between boundary Liouville conformal field theory in both its classical and random manifestations through this comprehensive lecture delivered by B. Cerclé from EPFL. Delve into the mathematical foundations of boundary Liouville CFT and examine how classical approaches relate to random geometric interpretations. Investigate the theoretical framework that bridges topological recursion, conformal field theory, and random geometry, gaining insights into cutting-edge research at the intersection of these mathematical disciplines. Analyze the specific properties and behaviors of boundary conditions in Liouville theory, understanding both deterministic and probabilistic perspectives. Discover how these concepts contribute to our understanding of two-dimensional quantum gravity and random surfaces, while exploring the mathematical tools and techniques used to study these complex systems.
